Rigidity percolation on aperiodic lattices

We studied the rigidity percolation (RP) model for aperiodic (quasi-crystal) lattices. The RP thresholds (for bond dilution) were obtained for several aperiodic lattices via computer simulation using the "pebble game" algorithm. It was found that the (two rhombi) Penrose lattice is always floppy in view of the RP model. The same was found for the Ammann's octagonal tiling and the Socolar's dodecagonal tiling. In order to impose the percolation transition we used so c. "ferro" modification of these aperiodic tilings. We studied as well the "pinwheel" tiling which has "infinitely-fold" orientational symmetry. The obtained estimates for the modified Penrose, Ammann and Socolar lattices are respectively: $p_{cP} =0.836\pm 0.002$, $p_{cA} = 0.769\pm0.002$, $p_{cS} = 0.938\pm0.001$. The bond RP threshold of the pinwheel tiling was estimated to $p_c = 0.69\pm0.01$. It was found that these results are very close to the Maxwell (the mean-field like) approximation for them.Comment: 9 LaTeX pages, 3 PostScript figures included via epsf.st

On Site Percolation on Correlated Simple Cubic Lattice

We consider site percolation on a correlated bi-colored simple cubic lattice. The correlated medium is constructed from a strongly alternating bi-colored simple cubic lattice due to anti-site disordering. The percolation threshold is estimated. The cluster size distribution is obtained. A possible application to the double 1:1 perovskites is discussed.Comment: 10 pages, 12 figures, Submitted to IJMP

An algorithm to calculate the transport exponent in strip geometries

An algorithm for solving the random resistor problem by means of the transfer-matrix approach is presented. Preconditioning by spanning clusters extraction both reduces the size of the conductivity matrix and speed up the calculations.Comment: 17 pages, RevTeX2.1, HLRZ - 97/9

Cluster counting: The Hoshen-Kopelman algorithm vs. spanning tree approaches

Two basic approaches to the cluster counting task in the percolation and related models are discussed. The Hoshen-Kopelman multiple labeling technique for cluster statistics is redescribed. Modifications for random and aperiodic lattices are sketched as well as some parallelised versions of the algorithm are mentioned. The graph-theoretical basis for the spanning tree approaches is given by describing the "breadth-first search" and "depth-first search" procedures. Examples are given for extracting the elastic and geometric "backbone" of a percolation cluster. An implementation of the "pebble game" algorithm using a depth-first search method is also described.Comment: LaTeX, uses ijmpc1.sty(included), 18 pages, 3 figures, submitted to Intern. J. of Modern Physics